a) Two perpendicular rays are drawn through a fixed point $P$ inside a given circle, intersecting the circle at points $A$ and $B$. Find the geometric locus of the projections of $P$ on the lines $AB$. b) Three pairwise perpendicular rays passing through the fixed point $P$ inside a given sphere intersect the sphere at points $A, B, C$. Find the geometrical locus of the projections $P$ on the $ABC$ plane
Problem
Source: Sharygin 2006 CR 24 (a) IX-X (b) X-XI
Tags: geometry, Locus, 3D geometry, projections, Plane, circle, sphere